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Proposal of Particular Criteria

1. Range of scales. Images are subjected to warps of varying intensity. We seek a perturbation framework that makes this intensity (magnitude) trivial to increase by a fixed and known amount. It should be flexible enough in terms of the scales supported or else obscenely large deformations cannot be investigated. One of the interesting properties to investigate is: at which point does the amount of perturbation become to difficult to detect and quantify?
2. Diffeomorphism. No folding, tearing, etc.
3. Invertibility. This is a useful property if one wishes to recover the images from their perturbed version. Being invertible is not, however, a much-required trait.
4. Large number of perturbation 'sources'. To make the effects of perturbation less local and more global, a large number of random processes, e.g. warps, need to be spread within the image boundaries.
5. No pixel condensation at images edges and corners. This 'stuffing' of pixels tends to happen when there is not sufficient freedom for pixels to be moved outside the image boundaries.
6. Stochastic. Perturbation needs to posses a stochastic nature. Points needs to be displaced by a random unit, which is drawn from a normal distribution
7. Predictable $E[\Delta_{average}]$. For any given point, the distribution of its displacements must be well-understood.
8. Similar distributions across the entire image. One would hope that displacements affect all parts of the image similarly. This may be difficult to assure.
9. Perturbation scales that increase in a well-behaved manner. $E[\Delta_{average}]$ should increase/decrease monotonically and also linearly or logarithmically (any other predictable curve which allows fitting should do) as function of the perturbation scale. If it increases too rapidly, valuable data might get neglected.
10. No re-re-sampling error. When images are warped (transformed), interpolated and re-sampled, there is a certain loss of detail, often visible in the form of blurring. There is an error associated with it too. Good perturbation will avoid errors (striving to reach 0) as errors add noise to the results.